Fill a solid corner topologically correct
If you have F2 addon enabled, here is a very magical trick.

Pressing F when F2 is enabled, several things will happen:


If 1 vertex is selected, it will create a face from the 2 edges connected with the vertex in the direction/position of the mouse cursor.
If 2 vertices or an edge is selected, it will try to created a quad face with the adjacent edges/vertices.  And the result doesn't need merging or 'remove double'.
If 3 or more edges are selected, it will simply create a face with selected edges.  Result can be an N-gon.